A177541 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, up, up.

1, 1, 2, 6, 24, 120, 720, 4990, 39520, 352080, 3484800, 37936800, 450606300, 5797965980, 80341280840, 1192794269400, 18889568419200, 317838157969125, 5662578565559400, 106488682710940108, 2107992477960872320, 43815112964794432080, 954074378001971825930

Offset: 0

Author

R. H. Hardin, May 10 2010

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..150

Crossrefs

Columns k=39,57 of A242784.

Programs

Maple

b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o=0, 1,
      add(b(u-j, o+j-1, [1, 3, 4, 1, 3, 3][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 2, 5, 6, 7][t]), j=1..o)))
    end:
a:= n-> `if`(n=0, 1, add(b(j-1, n-j, 1), j=1..n)):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 20 2013

Mathematica

b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
     Sum[b[u - j, o + j - 1, {1, 3, 4, 1, 3, 3}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 2, 5, 6, 7}[[t]]], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 19 2022, after Alois P. Heinz *)

Formula

a(n) ~ c * d^n * n!, where d = 0.98977300089321592191180343193285102663621683..., c = 1.06422234334396404091033045795479059186356... . - Vaclav Kotesovec, Jan 17 2015

Extensions

a(17)-a(22) from Alois P. Heinz, Oct 20 2013